I just replaced my NiMh battery with a rechargeable coin cell 3v 65mah battery and the x68000 is working super fine!
Good news - glad you found a solution!
I went with the Varta Nimh battery, linked in a previous post.
Just fitted it yesterday and it has passed it's first test; charged for 24hrs then the x68k was unplugged for a few hours - SRAM was still intact when i rebooted.
Will let it charge for another night and then unplug for 24hrs and see how it performs.
BTW. The Ni-Cd that i removed appears to be fine. I have just tested its voltage and its around 3.6v - cant say i expected that.